Fractional Calculus From Theory To Applications
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The Fractional Calculus Theory And Applications Of Differentiation And Integration To Arbitrary Order
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Author :
language : en
Publisher: Elsevier
Release Date : 1974-09-05
The Fractional Calculus Theory And Applications Of Differentiation And Integration To Arbitrary Order written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-09-05 with Mathematics categories.
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Fractional Calculus Theory And Applications
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Author : Francesco Mainardi
language : en
Publisher: MDPI
Release Date : 2018-09-20
Fractional Calculus Theory And Applications written by Francesco Mainardi and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Mathematics categories.
This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics
Fractional Calculus Theory And Applications
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Author : Francesco Mainardi (Ed.)
language : en
Publisher:
Release Date :
Fractional Calculus Theory And Applications written by Francesco Mainardi (Ed.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Fractional Calculus From Theory To Applications
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Author : Christos Volos
language : en
Publisher: BoD – Books on Demand
Release Date : 2025-05-28
Fractional Calculus From Theory To Applications written by Christos Volos and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-28 with Mathematics categories.
Over the last decade, research activity in the field of fractional calculus has surged, resulting in applications across a wide range of scientific disciplines. From the physics of diffusion and transport phenomena to control theory and financial systems, fractional calculus has proven valuable in numerous domains, capturing the interest of the scientific community. Therefore, this book comprises six chapters, each with the purpose of providing a brief overview of the subject of fractional calculus and its recent developments in theory and applications. This book aims to serve as an updated and handy reference for university professors, graduate students, laboratory researchers, as well as physicists and applied mathematicians who are interested in studying fractional calculus and its applications.
Fractional Calculus
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Author : Varsha Daftardar-Gejji
language : en
Publisher: ALPHA SCIENCE INTERNATIONAL LIMITED
Release Date : 2013-07-26
Fractional Calculus written by Varsha Daftardar-Gejji and has been published by ALPHA SCIENCE INTERNATIONAL LIMITED this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-26 with Mathematics categories.
FRACTIONAL CALCULUS: Theory and Applications deals with differentiation and integration of arbitrary order. The origin of this subject can be traced back to the end of seventeenth century, the time when Newton and Leibniz developed foundations of differential and integral calculus. Nonetheless, utility and applicability of FC to various branches of science and engineering have been realized only in last few decades. Recent years have witnessed tremendous upsurge in research activities related to the applications of FC in modeling of real-world systems. Unlike the derivatives of integral order, the non-local nature of fractional derivatives correctly models many natural phenomena containing long memory and give more accurate description than their integer counterparts.The present book comprises of contributions from academicians and leading researchers and gives a panoramic overview of various aspects of this subject: Introduction to Fractional Calculus Fractional Differential Equations Fractional Ordered Dynamical Systems Fractional Operators on Fractals Local Fractional Derivatives Fractional Control Systems Fractional Operators and Statistical Distributions Applications to Engineering
Fractional Calculus Theory And Applications
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Author : Gerald Paterson
language : en
Publisher:
Release Date : 2019-06-10
Fractional Calculus Theory And Applications written by Gerald Paterson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-10 with categories.
Fractional calculus falls under the domain of mathematical analysis. It focuses on the study of the differentiation operator in terms of real and complex number powers. Fractional calculus has various applications across other scientific fields such as polymer chemistry through structural damping models, in quantum theory through the analysis of Schrödinger's equation, etc. This book elucidates new techniques and their applications in a multidisciplinary manner. The chapters provide significant information of this field to help develop a good understanding of fractional calculus and related fields. It also attempts to understand the multiple branches that fall under this discipline and how such concepts have practical applications. It aims to serve as a resource guide for students and experts alike as well as contribute to the growth of the discipline.
Functional Fractional Calculus
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Author : Shantanu Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-01
Functional Fractional Calculus written by Shantanu Das and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Technology & Engineering categories.
When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions. Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.” This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.
Recent Developments In Fractional Calculus Theory Applications And Numerical Simulations
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Author : Lakhveer Kaur
language : en
Publisher: Springer Nature
Release Date : 2025-05-30
Recent Developments In Fractional Calculus Theory Applications And Numerical Simulations written by Lakhveer Kaur and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-30 with Technology & Engineering categories.
This book discusses recent developments in fractional calculus and fractional differential equations in a very elaborative manner and is of interest to research scholars, academicians and scientists who want to enhance the knowledge in the context of new insights and mathematical ideas in fractional calculus and its emerging applications in various fields. It focuses on strengthening the existing results along with identifying the practical challenges encountered. The purpose of this collection is to provide comprehension of articles that reflect recent mathematical results as well as some results in applied sciences untouched by the tools and techniques of fractional calculus along with their modelling and computation having applications in diverse arenas.
Fixed Point Theory And Fractional Calculus
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Author : Pradip Debnath
language : en
Publisher: Springer Nature
Release Date : 2022-05-10
Fixed Point Theory And Fractional Calculus written by Pradip Debnath and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-10 with Mathematics categories.
This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.
Fractional Calculus
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Author : Varsha Daftardar-Gejji
language : en
Publisher:
Release Date : 2014
Fractional Calculus written by Varsha Daftardar-Gejji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Fractional calculus categories.
Deals with differentiation and integration of arbitrary order. The book comprises contributions from academics and leading researchers and gives a panoramic overview of various aspects of the subject.